Write a program in \(\mathrm{R}\) that simulates \(b\) samples of size \(n\) from an EXPONENTIAL(1) distribution. For each of the \(b\) samples compute the minimum value of the sample. When the \(b\) samples have been simulated, a histogram of the \(b\) sample minimums should be produced. Run this simulation for \(n=5\), \(10,25,50\), and 100 with \(b=10,000\) and discuss the resulting histograms in terms of the theoretical result of Example 4.3.

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Example 4.3. Let {X} be a sequence of independent random variables where the distribution function of X, is Fn(2) = - exp(x) for x = [0, ), 10 for x = (-0,0).